Question: Determine the value of the following complex number power. Your answer will be plotted in orange. $ ({ e^{5\pi i / 6}}) ^ {4} $
Solution: Since $(a ^ b) ^ c = a ^ {b \cdot c}$ $ ({ e^{5\pi i / 6}}) ^ {4} = e ^ {4 \cdot (5\pi i / 6)} $ The angle of the result is $4 \cdot \frac{5}{6}\pi$ , which is $\frac{10}{3}\pi$ Our result is $ e^{4\pi i / 3}$.